X-rays Production by Electrons
X-rays were first observed by Wilhelm Roentgen in 1895, a German scientist who found them by accident
when experimenting with electron beams and vacuum tubes. The wavelength of a 10KeV X-ray is quite
-10
small, λ =1240eVnm/10000eV= 0.124 nm (1 Angsrom=10 m), allowing it readily to penetrate matter.
Roentgen found that X-rays were copiously produced by stopping electrons in a heavy metal target of
high-Z material. The generated x-ray spectra is composed of two components.
x-rays
electron
beam
Metal
target
(a) Continuous bremsstrahlung portion. When charged particles are accelerated (de-accelerated) they
can spontaneously emit photons (X-rays) in the field of a neighboring atom.
Line Spectra
Ee
Continuous Spectra
= Ee’ + Eγ
Eγ−max= Ee
EX-ray
When Ee’ = 0,
from 0 to Ee.
Eγ is a maximum. When Ee’ = Ee,
Eγ = 0 a minuimum. So the X-ray spectra ranges ,
(b) an X-ray Line Spectra described by the Bohr model. For a many electron atom the inner electrons
shield the nucleus and a Zeff must be substituted for Z.
13.6eV
!!!!!Energy!levels!of !a!hydrogen " like!atom!of !ch arg e!Z
n2
1
1
!!Z eff 2 ! 13.6eV !(! 2 " 2 )!!!!!!
n1 n2
En !!Z eff 2 !
#EL$
Zeff takes in to account the effective shielding of the nucleus by inner oribital electrons and other spinorbit and spin-spin effects.
In a typical electron x-ray tube, electrons are accelerated to the target by Vacc = 10’s of KVolts of
potential. A 100KV x-ray tube will produce at best 10 KeV X-rays !
K,L,M x-rays are produced in materials when inner atomic electrons are dislodged or ionized. Following
the Bohr model, Mosely predicted x-rays would follow the pattern:
1 1
EK! !!(Z " 1) # 13.6eV !(! 2 " 2 )!
1 2
1 1
EK $ !!(Z " 6)2 # 13.6eV !(! 2 " 2 )!
1 3
1
1
EL! !!(Z " 6)2 # 13.6eV !(! 2 " 2 )!
2
3
1
1
EL $ !!(Z " 6)2 # 13.6eV !(! 2 " 2 )!
2
4
etc.
n=5
2
n=4
n=3
n=2
n=1
Mα Mβ Mγ
Lα Lβ Lγ
Kα Kβ Kγ
Figure 1: The bremsstrahlung is caused by the de-acceleration of the electron in the metal. The x-ray lines
are from the filling of inner core electrons that have been displaced.
Computed Tomography (CT)
The attenuation of X-rays passing through an object can be used for imaging – computed tomography. For
a monoenergetic x-ray beam and a variable density absorber we can integrate over the line of sight of the
beam and obtain the image after many measurements are made. A typical scenario of a CT scan is shown
below.
!
I x, y = I 0 !e "
µ ( x, y)! s
source
!!!!!
ln(I 0 / I x, y )!=! " µ (x, y)ds
!1
µ (x, y) =!! #$ ln(I 0 / I x, y )! %& '!x-ray!image
detector
Questions to Answer:
1) Estimate the energy of the Kα X-ray in Pb.
2) A technique of identifying trace elements in a sample such as blood serum is to expose it to protons of a
few MeV in energy. The protons excite X-ray transitions in the heavy metals in the serum. Estimate the the
energy of the Kα X-ray emission from Cu and Zn and compare to their accepted values. 8.04 keV and
8.64keV respectively